Kinetics of cation ordering in synthetic Mg[Al.sub.2][O.sub.4] spinel

The time and temperature evolution of intracrystalline Mg-Al exchange in synthetic Mg[Al.sub.2][O.sub.4] spinel was studied by single-crystal X-ray diffraction of quenched samples, with the aim of contributing to rock cooling-rate estimation. Flux-grown, homogeneous crystals (0.1 mm in size) were annealed at 1000 [degrees]C and then were isothermally ordered at 900, 800, and 700 [degrees]C for 10 seconds to 40 days. The cation ordering process was investigated by measuring the spinel O atom positional parameter u, which had been previously demonstrated to be closely related to the inversion [chi] at equilibrium by the linear equation ([R.sup.2] = 0.995): [chi] = 21.396 - 80.714 u. From [chi] = 0.27 after annealing runs, the inversion decreased with time for all of the three ordering runs, and equilibrium was reached after about 4 min at [TAU] = 900 [degrees]C ([chi] = 0.25), about 55 min at [TAU] = 800 [degrees]C ([chi] = 0.23), and about 700 min at [TAU] = 700 [degrees]C ([chi] = 0.21). The Mueller kinetic model was satisfactorily applied to the experimental data. Solution of Mueller's integral gave the kinetic ordering constants [[KAPPA].sub.900] = 1.12 [+ or -] 0.57, [[KAPPA].sub.800] = 0.112 [+ or -] 0.047, and [[KAPPA].sub.700] = 0.0171 [+ or -] 0.0045 [min.sup.-1], corresponding to [t.sub.1/2] of 0.6, 6.2, and 40.5 min, respectively. The linear dependence of [KAPPA] with temperature ([R.sub.2] = 0.99) was observed, and may be expressed by the Arrhenius equation: In [KAPPA] = 20.189 - 23722/[TAU] ([KAPPA]) An activation energy of 197 [+ or -] 22 kJ/mol was obtained for the intracrystalline Mg-Al ordering reaction, which compares well with the value of 217 kJ/mol reported in the recent literature for Mg-[Fe.sup.3+] exchange in spinels.